Air Columns: And Toneholes- Principles For Wind Instrument Design

Ensure the mouthpiece or reed matches the air column's resistance.

Successful wind instrument design relies on three core axioms: Ensure the mouthpiece or reed matches the air

The open end does not behave as a perfect pressure node. Air outside the tube moves too, effectively lengthening the pipe. This is approximately 0.6 × radius for a flanged end (like a tonehole) and 0.85 × radius for an unflanged end (the bell). For short tubes (piccolo), end correction can be a significant fraction of total length. This is approximately 0

A single open tonehole acts as a complex acoustic impedance barrier consisting of: It radiates slightly past the opening

Sound doesn't stop exactly at the end of the tube or the center of a hole. It radiates slightly past the opening.

An instrument tuned in equal temperament is a series of compromises. Each tonehole must be sized and positioned so that: